Let $\ A,B $ be a poisson process with $\ \lambda = 2 $ in a timeframe of $\ 1 $ minute. Both are independent variables. Let $\ T $ = time that has passed from $\ 0 $ until the occurrence of the first event of $\ A $
I need to compute $\ P(T > 0.25) $
According to the solution given, $\ T \sim exp(2) $ and I can not understand why.
I found those two questions : https://stats.stackexchange.com/questions/2092/relationship-between-poisson-and-exponential-distribution & What is the difference between a Poisson and an Exponential distribution?
So I understand that time between two events of a poisson process is exponentially distributed yet I can't understand how to compute the parameter? In this question it means I have a event every 30 seconds. So if I understand correctly the time between events has a mean of $\ 30 $ seconds so $\ T \sim exp(30) $ ?